TIJUANA, Mexico >> Migrants in a caravan of Central Americans scrambled today to reach the U.S. border, arriving by the hundreds in Tijuana, while U.S. authorities across the border were readying razor wire security barriers.

Mexican officials in Tijuana were struggling to deal with a group of 357 migrants who arrived aboard nine buses Tuesday and another group of 398 that arrived today.

“Mexico has been excellent; we have no complaint about Mexico. The United States remains to be seen,” said Josue Vargas, a migrant from Honduras who finally pulled into Tijuana today after more than a month on the road.

U.S. Defense Secretary Jim Mattis, meanwhile, went to visit U.S. troops posted to the border in south Texas and said the deployment provides good training for war. President Donald Trump has said the caravan of migrants amounts to an “invasion.”

That didn’t deter arriving groups of Central Americans from going to a stretch of border fence in Tijuana to celebrate.

On Tuesday, a couple of dozen migrants scaled the steel border fence to celebrate their arrival, chanting “Yes, we could!” and one man dropped over to the U.S. side briefly as border agents watched from a distance. He ran quickly back to the fence.

Tijuana’s head of migrant services, Cesar Palencia Chavez, said authorities offered to take the migrants to shelters immediately, but they initially refused.

“They wanted to stay together in a single shelter,” Palencia Chavez said, “but at this time that’s not possible” because shelters are designed for smaller groups and generally offer separate facilities for men, women and families.

But he said that after their visit to the border, most were taken to shelters in groups of 30 or 40.

With a total of three caravans moving through Mexico including 7,000 to 10,000 migrants in all, questions arose as to how Tijuana would deal with such a huge influx, especially given U.S. moves to tighten border security and make it harder to claim asylum.

Buses and trucks today carried some migrants into the state of Sinaloa along the Gulf of California and further northward into the border state of Sonora.

The bulk of the main caravan appeared to be about 1,100 miles from the border, but was moving hundreds of miles per day.

The Rev. Miguel Angel Soto, director of the Casa de Migrante — House of the Migrant — in the Sinaloa capital of Culiacan, said about 2,000 migrants had arrived in that area. He said the state government, the Roman Catholic Church and city officials in Escuinapa, Sinaloa, were helping the migrants.

The priest also said the church had been able to get “good people” to provide buses for moving migrants northward. He said so far 24 buses had left Escuinapa on an eight-drive to Navojoa in Sonora state. Small groups were reported in the northern cities of Saltillo and Monterrey, in the region near Texas.

From Sonora, some migrants said they had already caught buses from to Tijuana.

About 1,300 migrants in a second caravan were resting at a stadium in Mexico City, where the first group had stayed last week. By early today, another 1,100 migrants from the third and last caravan had also arrived at the stadium.

Like most of those in the third caravan, migrant Javier Pineda is from El Salvador, and hopes to reach the United States. Referring to the first caravan nearing the end of the journey, Pineda said “if they could do it, there is no reason why we can’t.”

It is unclear whether the two caravans would merge or when they would set out on the road north.

Many say they are fleeing poverty, gang violence and political instability in the Central American countries of Honduras, Guatemala, El Salvador and Nicaragua.

Mexico has offered refuge, asylum or work visas, and its government said Monday that 2,697 temporary visas had been issued to individuals and families to cover them during the 45-day application process for more permanent status. Some 533 migrants had requested a voluntary return to their countries, the government reported.

The U.S. government said it was starting work Tuesday to “harden” the border crossing from Tijuana ahead of the caravans.

Customs and Border Protection announced it was closing four lanes at the busy San Ysidro and Otay Mesa ports of entry in San Diego, California, so it could install infrastructure.

That still leaves a substantial path for the tens of thousands of people who cross daily: Twenty-three lanes remain open at San Ysidro and 12 at Otay Mesa.

San Ysidro is the border’s busiest crossing, with about 110,000 people entering the U.S. every day. That traffic includes some 40,000 vehicles, 34,000 pedestrians and 150 to 200 buses.